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Institute of Electrical Power Engineering
Wrocáaw University of Technology
WybrzeĪe WyspiaĔskiego 27, 50-370 Wrocáaw, Poland
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© Copyright by Oficyna Wydawnicza Politechniki Wrocáawskiej, Wrocáaw 2013
OFICYNA WYDAWNICZA POLITECHNIKI WROCàAWSKIEJ
WybrzeĪe WyspiaĔskiego 27, 50-370 Wrocáaw
http://www.oficyna.pwr.wroc.pl
e-mail: oficwyd@pwr.wroc.pl
zamawianie.ksiazek@pwr.wroc.pl
ISSN 2084-2201
Drukarnia Oficyny Wydawniczej Politechniki Wrocáawskiej. Order No. 706/2013.
voltage stability,
transformer tap changer
Bartosz BRUSIàOWICZ*
Janusz SZAFRAN*
INFLUENCE OF TRANSFORMER TAP CHANGER OPERATION
ON VOLTAGE STABILITY
The paper concerns influence of transformer tap changer regulation on secondary voltage level
and voltage stability margin of receiving node. At the beginning there are presented general information about voltage stability and tap changer. Voltage value of secondary terminals of transformer can
be regulated using tap changer. This regulation also affects the calculation of Thevenin equivalent
parameters seen from the secondary terminals. Changes of equivalent parameters cause a change of
voltage stability conditions. Simulation studies of this influence for various types of load have been
done. Selected simulation results are presented in the paper. At the end there are placed conclusions
from the performed studies.
1. INTRODUCTION
Electricity delivered to customers should have appropriate quality. Required parameters are defined in European Standard EN 50160 [1]. One of the power quality
parameters is the voltage value. The voltage variations can be caused by normal operation of power system – changes of power system configuration or parameters of
loads. The power system can be designed to maintain the value of voltage in acceptable limits despite of these changes. However, randomly situations where these limits
are exceeded can occur. To ensure constant voltage level, some of power system nodes
should have a voltage control systems. This regulation, what is obvious, also affects
other parameters of the operating point of power system node. The most commonly
used methods of voltage adjustment are: voltage tap changer, reactive power compensation and undervoltage load shedding. This paper refers only to analysis of the influence of transformer tap changer operation on voltage level and voltage stability.
_________
* Institute of Electrical Power Engineering, Wrocáaw University of Technology, Wrocáaw Poland.
B. BRUSIàOWICZ, J. SZAFRAN
26
Voltage stability is defined by IEEE in the following way: “Voltage stability is the
ability of a system to maintain voltage so that when load admittance is increased load
power will increase and so that both power and voltage are controllable” [2].
Margin of this stability can be determined using a full model of the power system
and the power flow calculations. Voltage characteristics of loads can be added for
such model. For each node stability margin can be calculated basing on changes of
parameters caused by voltage variations e.g. dǻQ/dV [3, 4].
To study voltage stability of selected power system receiving node, it is more convenient to use a simplified Thevenin equivalent model. In this model part of power
system seen from the node may be replaced by ideal voltage source E and system impedance ZS (Fig. 1).
ZS
ZL
Power
System
E
I
V
ZL
V
I
Fig. 1. Thevenin model
Parameters of stable operating point of presented Thevenin circuit are defined by
the following equations [5]:
E
V
S
1 W 2W cos E
2
,
E 2W
.
Z S (1 W 2 2W cos E )
(1)
(2)
where: V – node voltage, S – load apparent power, W = ZS/ZL, ZS – system impedance,
ZL – load impedance, E = MS – ML, MS and ML – system and load phase angle.
Voltage stability limit occurs at the point of maximum power transfer [6]. In this
point, the equation (3) is true. Thus, to calculate voltage stability margin it is more
practical to use equation (4).
ZS
'W
1W
ZL ,
1
(3)
ZS
.
ZL
(4)
influence of Transformer Tap Changer Operation on Voltage Stability
27
Value of load impedance is greater than system impedance, so W parameter is changing from 0 to 1. The power system receiving node is stable if value of W is lower than 1.
In the literature various methods of W parameter calculation can be found. These
methods often use only locally available measurements of voltage and current. For
example W parameter can be calculated using: equations of Thevenin model [6], derivatives of apparent load power against the node voltage dS/dV [7] or node voltage
against load admittance dV/dY [8].
2. TRANSFORMER TAP CHANGER
To regulate the secondary voltage level separated coils of winding are connected to
the tap changer at one of the transformer site, usually at the primary. Operation of the
tap changer modifies the total number of active coils of primary winding. For a fixed
number of coils at secondary winding, this action causes change of transformer voltage ratio.
Types of tap changers are divided into: De-Energized Tap Changer (DETC) and
Load Tap Changer (LTC) [9]. DETC regulators are used in systems where need of
voltage level changing occurs relatively rare. If the voltage value changes often LTC
systems are used.
For Thevenin model (Fig. 1) voltage regulation using transformer tap changer can
be added (Fig. 2a). In this model, the winding and core losses are omitted. Level of
secondary voltage depends on the position of tap changer g according to equation (5)
g
VL
.
V1
(5)
To eliminate the tap changer from presented model, Thevenin parameters to various windings of transformer can be calculated. The system impedance ZS and voltage
source E can be converted to the secondary winding according to the formula (6).
Figure 2b shows Thevenin model with calculated parameters.
ZS ' ZS * g 2
a)
E
ZS
b)
g
V1
E' E * g
VL
ZL
E
Fig. 2. Thevenin model with tap changer
(6)
ZS*g
E*g
2
VL
ZL
B. BRUSIàOWICZ, J. SZAFRAN
28
Taking into account transformer ratio g in voltage equation (1), secondary voltage
can be described by following formula:
VL
Eg
1 Wg
2Wg
2 2
2
cos E
.
(7)
From equations (5) and (7) primary voltage can be calculated in the following way:
V1
VL
g
1 Wg
E
2Wg
2 2
2
cos E
.
(8)
Above presented equations show that the change of tap changer position affects
primary and secondary transformer voltage. When g parameter increases, secondary
voltage raises and primary voltage decreases. Figure 3 shows an example of this relation. Curves have been plotted for following parameters: E = 1, W = 0.3, MZS = 85°,
MZL = 15°. Derivatives of primary and secondary voltages against transformer ratio g
and sum of these derivatives are shown in Figure 3b.
a)
b)
1
0.8
0.9
dV/dg [p.u.]
V [p.u.]
0.6
0.8
V1
VL
0.7
0.8
0.9
1
g
1.1
0.4
0.2
0
dV1/dg
dVL/dg
-0.2
1.2
-0.4
0.8
0.9
1
g
1.1
1.2
Fig. 3. Changes of primary and secondary voltage a) and derivatives b) for W = 0.3, E = 70°
The derivative of the voltage against g ratio can be used as a criterion for tap
changer operation blocking. The blocking should be performed when the changing tap
changer does not provide desired effect. Such criterion has been described in literature
[8]. The tap changer should be blocked when the derivatives of voltages are equal.
Therefore, tap changer operation is allowed when the condition (9) is true. When this
condition is not fulfilled, g ratio changing causes a greater decrease of primary voltage
than increase of the secondary voltage. In such case, it is reasonable to block the tap
changer.
influence of Transformer Tap Changer Operation on Voltage Stability
29
dVL dV1
!0
dg
dg
(9)
3. SIMULATION RESULTS
a)
b)
1.2
1.1
1
dV/dg [p.u.]
V [p.u.]
Simulations of influence of tap changer operation on primary and secondary voltage changes have been performed. The following parameters of Thevenin model have
been assumed: E = 1 |ZS| = 1 MZS = 85°. Load angle MZL, as in the previous case, has
been 15°, so ȕ angle has amounted 70°. Simulations have been performed for different
values of the load impedance. The W parameter has taken following values: W = 0,1;
0,3; 0,5 and 0,7. Figures 4–7 show changes of the primary and secondary voltage and
derivatives of these changes.
1
0.9
V1
VL
0.8
0.8
0.9
1
g
1.1
0.8
0.6
dV1/dg
dVL/dg
0.4
0.2
0
-0.2
0.8
1.2
0.9
1
g
1.1
1.2
Fig. 4. Changes of primary and secondary voltage a) and derivatives b) for W = 0.1, E = 70°
a)
1
b)
1
0.8
V [p.u.]
dV/dg [p.u.]
0.9
0.8
V1
VL
0.7
0.8
0.9
1
g
1.1
0.6
0.4
0.2
0
dV1/dg
dVL/dg
-0.2
1.2
-0.4
0.8
0.9
1
g
1.1
1.2
Fig. 5. Changes of primary and secondary voltage a) and derivatives b) for W = 0.3, E = 70°
B. BRUSIàOWICZ, J. SZAFRAN
30
a)
0.9
b)
dV 1/dg
dVL /dg
dV/dg [p.u.]
V [p.u.]
0.8
0.8
V1
VL
0.7
0.8
0.9
1
g
0.4
0
-0.4
1.1
0.8
1.2
0.9
1
g
1.1
1.2
Fig. 6. Changes of primary and secondary voltage a) and derivatives b) for W = 0.5, E = 70°
a)
b)
0.6
V1
VL
dV1/dg
dVL/dg
0.4
dV/dg [p.u.]
V [p.u.]
0.8
0.7
0.2
0
-0.2
-0.4
0.6
0.8
0.9
1
g
1.1
1.2
-0.6
0.8
0.9
1
g
1.1
1.2
Fig. 7. Changes of primary and secondary voltage a) and derivatives b) for W = 0.7, E = 70°
The presented plots show that the lean of curves depends on the W parameter. For
small values of W (Fig. 4) regulation of secondary voltage VL does not change significantly the primary voltage V1. Secondary voltage derivative dVL/dg is positive and
primary voltage derivative dV1/dg is negative. In the operational range g = 0.8:1.2 sum
of these derivatives will be greater than zero. So the condition (9) is true. Also, for
W = 0.3 in the operational range sum of derivatives does not reach zero. Approaching
to the end of range, the sum is close to zero. However, the tap changer should not be
blocked. For W = 0.5 sum of voltages derivatives reaches zero for g = 0.97. When tap
changer is in neutral position g=1 and such load occurs, any increase of the secondary
voltage results in a large decreasing of primary voltage so the regulation is not effective. When W = 0.7 regulation of voltage is not effective over the operational range.
Different rates of changes of derivatives for various values of W parameter are
caused by the increase of voltage and apparent power. Therefore, the operating point
influence of Transformer Tap Changer Operation on Voltage Stability
31
is moved both upwards and in the direction of maximum power transfer. These contingencies for various values of W parameter are shown in Fig. 8. The solid line is the
curve plotted for g = 1. Dashed lines indicate the transformer ratio changes to g = 0.8
and g = 1.2. Load characteristics are marked by dotted lines. Fig. 8 shows that for
rising initial W parameter, increase rate of secondary voltage caused by tap changer
operation is getting smaller and increase rate of apparent power is growing.
1.2
W=0.1
g=1.2
V [p.u.]
1
W=0.3
g=1
W=0.5
0.8
g=0.8
0.6
W=0.7
0.4
0
0.1
0.2
S [p.u.]
0.3
0.4
Fig. 8. Nose curves and load characteristics
It is obvious that changes of V1 and VL voltages also depend on the angle of the
load impedance. For angles close to zero or negative (capacitive load) the initial voltage drop is smaller and regulation brings greater effect. Figure 9 shows sum of derivatives for W = 0.4 and three values of the load impedance angle. In the tap changer
operational range blocking should be performed only for angle amounting MZL = 15°.
ijL=15
ijL =0
ijL=-15
1
dV/dg [p.u.]
0.8
0.6
0.4
0.2
0
-0.2
0.8
0.9
1
g
1.1
1.2
Fig. 9. Sum of derivatives for various load angles
B. BRUSIàOWICZ, J. SZAFRAN
32
Assuming that the limit of voltage stability occurs when W = 1 and that the change
of tap changer position affects calculation of system impedance ZS, equation (10) can
be written. Equation (10) can be transformed to formula (11). This formula can be
used to calculate limit tap changer position for which the circuit reaches the limit of
stability. Changes of glim according to value of W variations are shown in Fig. 10.
W
W1 * g 2
g lim
1
W1
1,
(10)
.
(11)
glim
3
2
1
0
0
0.2
0.4
W
0.6
0.8
1
Fig. 10. Changes of glim according to W variations
It can be seen that the values of glim are greater than those resulting from quoted
criterion based on measurement of voltage derivatives. In the presented example, for
W = 0.5 blocking tap changer should be performed for g = 1.125 (Fig. 6). For this
level of W parameter, value of glim = 1.4 (Fig. 10). This confirms the validity of voltages derivatives criterion. However, between the values of g resulting from this criterion and glim there is an area where the regulation might be performed.
4. NONLINEAR LOADS
Previous considerations have been carried out assuming that the load impedance
is linear. However, in reality, the value of impedance depends on the voltage level.
Example dependences are presented in the IEEE publication [9].
The simplest way of describing nonlinear load model is the exponential equation (12).
influence of Transformer Tap Changer Operation on Voltage Stability
33
D
ZL
§V ·
Z L 0 ¨¨ ¸¸
© V0 ¹
(12)
where: ZL0 – rated impedance, D – exponent of voltage characteristic.
Examples of basic models (constant impedance, current and power) are shown in
Fig. 11. The Figure shows that changes of voltage and apparent power are different for
various load models. It can be concluded that the impact of tap changer regulation
depends on Į exponent (equation (12)).
1.2
1
V [p.u.]
0.8
0.6
0.4
0.2
0
0
0.1
0.2
S [p.u.]
0.3
0.4
Fig. 11. Nose curves and load characteristics
For the fixed parameters of Thevenin model value of W depends only on the load
impedance. In nonlinear model this impedance is changing according to value of secondary voltage. Converting the load impedance on the primary voltage and including
dependence on voltage equation (13) can be obtained.
W1
ZS
ZL
ZS
V g D
Z L 0 1 21
g1
(13)
where: V1 = V1/V0; V0 – rated voltage.
The W parameter strongly depends on transformer ratio g. Equation 13 can be also
written for changed value of g2. From both equations, system impedance ZS can be
determined. Comparing and transforming these two equations formula (14) can be
calculated. W2/W1 parameter represents variations of W according to change of g and
D exponent of load model.
W2
W1
§ g2 ·
¨¨ ¸¸
© g1 ¹
2 D
(14)
B. BRUSIàOWICZ, J. SZAFRAN
34
Changing the value of tap changer position g, curves corresponding to changes of
W2/W1 parameter for fundamental load models have been plotted. These models have
been: D = 0 – constant impedance, D = 1 – constant current, D = 2 – constant power.
Obtained curves are shown in Figure 12.
1.4
Į=0
Į=1
Į=2
W2/W1
1.2
1
0.8
0.6
0.8
0.9
1
g
1.1
1.2
Fig. 12. Chages of W2/W1 parameter according to g variations
From Figure 12 it can be noticed that increase of W parameter is greater when D
exponent is lower. The largest increase is for the constant impedance load and the
lowest for constant power model. This contingency is similar to that shown in
Figure 11. The greatest increase of load apparent power (getting closer to the stability
limit) is for constant impedance model. If the load model is constant power, tap
changer operation changes only value of voltage.
To transform load impedance to primary voltage, value of the impedance should be
divided by squared transformer ratio g. Value of impedance of constant power model
depends on squared secondary voltage. This voltage depends on g parameter. Therefore, W parameter is not changed.
Additional tests similar to those in section 3, using constant power model have
been made. Formula (12) is nonlinear, so to perform simulations the method of solving
nonlinear equations has been chosen. Aitken iterative algorithm has been used [10].
From Figure 13 it can be noticed that rising g parameter causes increase of secondary voltage level with no change of primary voltage. The derivative of primary voltage is zero and derivative of secondary voltage is positive. Therefore, the sum of derivatives will never reach zero. For constant power model, operation of tap changer
can be carried out over entire range of regulation regardless of the W parameter and
angle of the load.
influence of Transformer Tap Changer Operation on Voltage Stability
a)
b)
0.8
V1
VL
0.6
dV/dg [p.u.]
V [p.u.]
0.9
35
0.8
0.7
dV 1/dg
dV L/dg
0.4
0.2
0
0.6
0.8
0.9
1
g
1.1
1.2
0.8
0.9
1
g
1.1
1.2
Fig. 13. Changes of primary and secondary voltage (a) and derivatives (b)
for W = 0.3, E = 70° – constant power model
When voltage regulation using tap changer for constant impedance model is performed the voltage stability conditions are the worst. For this model the apparent
power varies with the square of the transformer ratio g. Constant power model is the
safest because the tap changer operation does not endanger safety of the node.
5. CONCLUSIONS
1. It is possible to block tap changer using quoted criterion when increasing secondary voltage level causes a significant decreasing of primary voltage. Blocking point
is determined by measuring the derivatives of these voltages according to transformer
ratio changes.
2. For each value of W parameter it is possible to calculate the critical transformer ratio. This value corresponds to transformer ratio which will result in loss of
voltage stability. In the paper glim is calculated assuming linear load impedance. For
other models, the critical value will be probably greater. Therefore, use of glim calculated for linear impedance to nonlinear models will result in greater safety margin
obtained.
3. Value of glim parameter is greater than g level arising from the quoted criterion.
Between them there is an area where the voltage regulation could be carried out
maintaining given stability margin.
4. The effect of tap changer operation depends on load model. The paper describes
the dependence of these effects according to value of Į exponent.
5. When voltage regulation using tap changer is performed it is required to determine the impact of these actions on value of voltage and voltage stability margin.
36
B. BRUSIàOWICZ, J. SZAFRAN
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